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Abstract

Previous work on two-treatment comparisons has shown that the use of optimal
response-adaptive randomisation with group sequential analysis can allocate more
patients to the better-performing treatment while preserving the overall type I
error rate. The sequence of test statistics for this adaptive design asymptotically
satisfi es the canonical joint distribution. The overall type I error rate can be controlled
by utilising the error-spending approach. However, previous work focused
on immediate responses. The application of the adaptive design to censored survival
responses is investigated and different optimal response-adaptive randomised
procedures compared. For a maximum duration trial, the information level at the
fi nal look is usually unpredictable. An approximate information time is defi ned.
Several treatments are often compared in a clinical trial nowadays. The adaptive
design generalised to multi-arm clinical trials is studied. First, a global test
is considered. The joint distribution of the sequence of test statistics no longer
has the canonical distribution. However, the joint distribution can be derived,
since the test statistic is a quadratic form of independent normal variables. Existing
critical boundaries are based on normal responses and known variances with
equal allocation and equal increments in information. Our results show that these
boundaries can be used approximately for designs with other types of responses,
unequal variances or unbalanced allocation. If the global null hypothesis is rejected, then pairwise comparisons are conducted
at the current and subsequent looks to investigate which treatment effects differ.
This is an analogue of Fisher's least signi cant difference method that can control
the family-wise error rate. The adaptive design can target any optimal allocation
to achieve some optimality criterion, and allows dropping of inferior treatments at
interim looks, which can be unequally spaced in information time. Optimal allocation
proportions after dropping arms are described. The power is not adversely
affected by unbalanced allocation.